How to make a green tea extract for cake flavoring?

I bought a box of green tea bags and dropped about 6 into simmering water. I dunked them a few times until the water color changed to what seemed a little strong, removed them and reduced the liquid until it just barely covered the bottom of my pan and was the color of coffee. It was so strong and bitter that I wondered if it would ruin a cake, but tried it anyway. Yesterday I baked a 3 egg yellow cake with about 1/4 cup of my extract substitute in place of milk. The cake tastes fine but I can't taste green tea. I shoudl mention that I got so busy with other things in the kitchen that I left the cake in about 10min too long, and it came out more like cookies than a cake. It's possible that had I not ruined the cake otherwise, it would have tasted like green tea, but I'm not very confident of that.

How do you get a green tea taste in a cake? Maybe I should leave out the yolks and try a white cake? It diodn't rise as well either, maybe I should test extract w/ litmus paper and adjust leavening as necessary?

I found a place called nuts online dot com. I haven't ordered from them nor to I attest to their legitimacy, honesty, or quality, but their alleged customers do in comments all over their site. It's possible it could be a scam site but I'd be willing to test them if I could figure out a way to safely pay for the order w/out exposing a credit/debit card. If anyone has experience with them I'd like to know. They have green tea powder that, according to what I read on Wikipedia, is exactly what I'm lookin for and it runs from 5.99 - 17.99 / pound! That's way less than a little tin of imported gourmet tea, and sounds more like what the people putting it in little tins pay for the product. What do you think?

I wouldn't pay more than 5.99 (USD) for a tin (i.e. my tin is 30 grams). Give or take a couple bucks however might be worth it for you, depending on your price-costing and use for the cake. I looked at the tin I had (30g) which I must have bought in Japan a zillion years ago because there is nothing written in English on it (and it's probably only good for cake these days ). The telephone number on the tin is: (075) 661-1691 if that helps.

Anyway...Matcha is the way to go I feel, and I wouldn't spend more than twice what I quoted above.

Good luck!!! I might just put my old tin of green tea to some use now, thanks.